well the subject title pretty much says it.
do spiders sleep? and if so when? do they like to sleep when its dark? or when its light?
or when they don’t move, is it just because they see you, and are pretending to be asleep until you go away?
Welcome aboard(s), fifi85!
Since spiders do not have any eyelids, I’d venture their rest phase is something like what fish go through. A quasi-trance or semi-dormancy sort of state.
As to why some insects or animals freeze when undergoing potential threat; This may be due to the fact that a moving prey is much easier for other (less well sighted) creatures to detect. We too often take our own excellent vision for granted in the animal world. Few other critters have the sort of full color stereo vision we humans have.
From the Australian Museum: Do Spiders Sleep?
And do they have bad dreams about us? I certainly hope so. Fair play and all that.